This has been discussed in other threads. Lee was offered command of an army, not all Union armies. He also had a learning curve - West Virginia was a failure, the Seven Days was miscoordinated. And his record on offense was not very good.
Most likely his career parallel's OTL's McDowell, sent into battle before the troops are really ready, makes his own mistakes, and is sidelined for the rest of the war. (Though he might be sent west instead and prove he was better than he initially appeared.)
Without Lee, there's a good chance Richmond falls to McClellan during the Peninsula Campaign. If Little Mac doesn't rest on his laurels, there's a good chance the war is shorter and less bloody.